Manuscript En05-C@1 · En05-C.tex · section · aa213ea6

Partitioned layers

Stage E: one-layer locality without product channels › Partitioned layers · lines 1368–1385

En05-C@1#eq:layercomposition

Let a finite site set $X$ have a partition $P_{s}$ at tick $s$ . The sites may be links of the gauge graph. Each block $b$ carries a specified internal Kraus device. Define the global Heisenberg layer by composition:

T_{s} = b \in P_{s} \prod T_{s, b} .

The order is irrelevant by Lemma lem:devicesupport. Equation (eq:layercomposition) is not a spatial tensor product.

For $Y \subseteq X$ , put

U_{s} (Y) = ⋃ {b \in P_{s} : b \cap Y \neq = \emptyset} .

Displayed formulas in this passage

En05-C@1#eq:layercomposition · line 1374
$T_{s} = b \in P_{s} \prod T_{s, b} .$
unlabeled · line 1382
$U_{s} (Y) = ⋃ {b \in P_{s} : b \cap Y \neq = \emptyset} .$

Nearby in this section

theorem: Theorem: Tensor-free one-layer support
remark: Remark: Countable locally finite substrates